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add parametric equations for eptrochoid

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Daniel Weschke
2019-11-04 10:49:49 +01:00
parent 254fa75498
commit b7887db0ac
6 changed files with 147 additions and 4 deletions
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51
docs/build/html/function.html vendored
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@@ -37,7 +37,7 @@
<p>Mathematical equations.</p>
<dl class="field-list simple">
<dt class="field-odd">Date</dt>
<dd class="field-odd"><p>2019-11-01</p>
<dd class="field-odd"><p>2019-11-02</p>
</dd>
</dl>
<span class="target" id="module-function"></span><dl class="function">
@@ -72,6 +72,55 @@ time t</p>
</div>
</dd></dl>
<dl class="function">
<dt id="function.epitrochoid">
<code class="sig-name descname">epitrochoid</code><span class="sig-paren">(</span><em class="sig-param">R</em>, <em class="sig-param">r</em>, <em class="sig-param">d</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/function.html#epitrochoid"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#function.epitrochoid" title="Permalink to this definition"></a></dt>
<dd><p>Epitrochoid</p>
<p>A point is attached with a distance d from the center of a circle
of radius r. The circle is rolling around the outside of a fixed
circle of radius R.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>R</strong> (<em>float</em>) – radius of the fixed interior circle</p></li>
<li><p><strong>r</strong> – radius of the rolling circle outside of the fixed circle</p></li>
<li><p><strong>d</strong> (<em>float</em>) – distance from the center of the exterior circle</p></li>
</ul>
</dd>
<dt class="field-even">Typre r</dt>
<dd class="field-even"><p>float</p>
</dd>
<dt class="field-odd">Results</dt>
<dd class="field-odd"><p>functions for x of theta and y of theta</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>tuple</p>
</dd>
</dl>
<div class="math notranslate nohighlight">
\[\begin{split}x(\theta) = (R + r)\cos\theta - d\cos\left(\frac{R+r}{r}\theta\right) \\
y(\theta) = (R + r)\sin\theta - d\sin\left(\frac{R+r}{r}\theta\right) \\
\theta = \left[0, 2\pi\right]\end{split}\]</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">*</span> <span class="o">*</span> <span class="o">*</span>
<span class="o">*</span> <span class="n">R</span> <span class="o">*</span>
<span class="o">*</span> <span class="o">*</span>
<span class="o">*</span> <span class="o">*</span> <span class="o">*</span> <span class="o">*</span>
<span class="o">*</span> <span class="o">*</span> <span class="o">*</span> <span class="n">r</span> <span class="o">*</span>
<span class="o">*</span> <span class="o">**</span> <span class="o">....</span> <span class="o">*</span>
<span class="o">*</span> <span class="o">**</span> <span class="n">d</span> <span class="o">*</span>
<span class="o">*</span> <span class="o">*</span> <span class="o">*</span> <span class="o">*</span>
<span class="o">*</span> <span class="o">*</span> <span class="o">*</span> <span class="o">*</span>
<span class="o">*</span> <span class="o">*</span>
<span class="o">*</span> <span class="o">*</span>
<span class="o">*</span> <span class="o">*</span> <span class="o">*</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">epitrochoid</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">)[:</span><span class="mi">1</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">theta_end</span> <span class="o">=</span> <span class="n">epitrochoid</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">)</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="function.hypotrochoid">
<code class="sig-name descname">hypotrochoid</code><span class="sig-paren">(</span><em class="sig-param">R</em>, <em class="sig-param">r</em>, <em class="sig-param">d</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/function.html#hypotrochoid"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#function.hypotrochoid" title="Permalink to this definition"></a></dt>